I think one way to change society's perceptions is for them to find out that... we live among them! We always have!
I've been living a very closeted existence. Even now, after coming out somewhat, I'm still very private. It occurred to me one day that the people in my city, and community, may be fooled into thinking that they live in some sort of cis-bubble - no gender bending here, no sir! Don't you know these are the suburbs?
There are some very public trans or cd people in the media, but I would bet good money that most of us are 'hidden in plain sight'. We're secretly agonizing in front of our mirrors, and then putting on gender-approved clothes when going out. So everyone (including me) is fooled into believing we live in such a mainstream society.
That's when I realized me presenting femme in public might be important not just for me, but for others out there. Sure, a bit startling for them, at first. But perhaps they may realize "oh, they're not just on TV, they're my neighbors..."
On a slight tangent: saw someone presenting mostly male, but with full feminine makeup at a very busy mall the other day. He seemed in his 20s. Made me smile. I wanted to stop and say something supportive, but it was busy and we just passed each other.